2015/08/13 by Ilya I. Bogdanov, Bogdanov, Ilya I., Alexander D. Matushkin +1
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #Metric Geometry (math.MG) #graph theory and CDMA systems #math.CO #math.GT #math.MG
paper · pdf · doi:10.48550/arxiv.1508.03185
in Russian
arxiv created 2015/08/13 · openalex publication_date 2015/08/13 · arxiv updated 2015/08/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we present short algebraic proofs of the Linear Conway--Gordon--Sachs and the Linear van Kampen--Flores theorems in the spirit of the Radon theorem on convex hulls. \bf Theorem. \it Take any n+3 general position points in ℝn. If n is odd, then there are two linked (n+1)/2-simplices with the vertices at these points. If n is even, then one can choose two disjoint (n+2)/2-tuples such that the interiors (n/2)-simplices with the vertices at these (n+2)/2-tuples intersect each other. This theorem is interesting even in case of small dimensions.